Cremona's table of elliptic curves

33984 = 2⁶ · 3² · 59

Field	Data	Notes
Atkin-Lehner	2+ 3- 59-	Signs for the Atkin-Lehner involutions
Class	33984s	Isogeny class
Conductor	33984	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	16384	Modular degree for the optimal curve
Δ	528519168 = 212 · 37 · 59	Discriminant
Eigenvalues	2+ 3-  0 -4  4  4  2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-2100,37024]	[a1,a2,a3,a4,a6]
Generators	[8:144:1]	Generators of the group modulo torsion
j	343000000/177	j-invariant
L	5.3086926409381	L(r)(E,1)/r!
Ω	1.6249803169041	Real period
R	1.633463675133	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	33984j1 16992g1 11328c1	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 33984s1

a2	a3	a5	a7	a11	a13	a17	a19	a23	a29	a31	a37	a41	a43	a47	a53	a59	a61	a67	a71	a73	a79	a83	a89	a97
+	-	0	-4	4	4	2	-4	4	0	2	0	2	-8	4	-12	-	8	-4	-6	2	4	-4	-10	-2

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Quadratic twists for elliptic curve 33984s1

-4	8	-3
33984j1	16992g1	11328c1

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Data from Elliptic Curve Data by J. E. Cremona.
Design inspired by The Modular Forms Explorer by William Stein.

Part of Computational Number Theory
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